| Title:
|
A practical solution to implement nonlinear output regulation via dynamic mappings (English) |
| Author:
|
Armenta, Carlos |
| Author:
|
Álvarez, Jorge |
| Author:
|
Márquez, Raymundo |
| Author:
|
Bernal, Miguel |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 (print) |
| ISSN:
|
1805-949X (online) |
| Volume:
|
55 |
| Issue:
|
2 |
| Year:
|
2019 |
| Pages:
|
385-401 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
This paper presents a novel error-feedback practical solution for real-time implementation of nonlinear output regulation. Sufficient and necessary conditions for both state- and error-feedback output regulation have been established for linear and nonlinear systems several decades ago. In their most general form, these solutions require solving a set of nonlinear partial differential equations, which may be hard or even impossible to solve analytically. In recent years, a methodology for dynamic calculation of the mappings required for state-feedback regulation has been put forward; following the latter, an error-feedback extension is hereby provided which, when combined with design conditions in the form of linear matrix inequalities, becomes suitable for real-time setups. Real-time results are presented for a nonlinear twin rotor MIMO system. Issues concerning the implementation as well as the solutions adopted, are discussed. (English) |
| Keyword:
|
nonlinear output regulation |
| Keyword:
|
linear matrix inequality |
| Keyword:
|
twin rotor |
| Keyword:
|
real-time |
| MSC:
|
93C10 |
| MSC:
|
93C95 |
| MSC:
|
93D05 |
| idZBL:
|
Zbl 07144944 |
| idMR:
|
MR4014593 |
| DOI:
|
10.14736/kyb-2019-2-0385 |
| . |
| Date available:
|
2019-09-30T15:10:37Z |
| Last updated:
|
2020-04-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147843 |
| . |
| Reference:
|
[1] Ahmed, Q., Bhatti, A. I., Iqbal, S.: Robust decoupling control design for twin rotor system using Hadamard weights..In: Control Applications, (CCA) and Intelligent Control, (ISIC), 2009 IEEE, pp. 1009-1014. 10.1109/cca.2009.5281000 |
| Reference:
|
[2] Bernal, M., Marquez, R., Estrada, V., Castillo, B.: An element-wise linear matrix inequality approach for output regulation problems..In: World Automation Congress (WAC) 2012, Puerto Vallarta 2012, pp. 1-6. |
| Reference:
|
[3] Bernal, M., Marquez, R., Estrada-Manzo, V., Castillo-Toledo, B.: Nonlinear output regulation via Takagi-Sugeno fuzzy mappings: A full-information LMI approach..In: IEEE International Conference on Fuzzy Systems 2012, pp. 1-7. 10.1109/fuzz-ieee.2012.6251202 |
| Reference:
|
[4] {Boyd}, S., Ghaoui, L. E., Feron, E., Belakrishnan, V.: Linear Matrix Inequalities in System and Control Theory..SIAM, Studies In Applied Mathematics 15, Philadelphia 1994. MR 1284712, 10.1137/1.9781611970777 |
| Reference:
|
[5] Byrnes, C. I., Isidori, A.: Limit sets, zero dynamics, and internal models in the problem of nonlinear output regulation..IEEE Trans. Automat. Control 48 (2003), 10, 1712-1723. MR 2021420, 10.1109/tac.2003.817926 |
| Reference:
|
[6] Byrnes, C. I., Isidori, A.: Nonlinear internal models for output regulation..IEEE Trans. Automat. Control 49 (2004), 12, 2244-2247. MR 2106753, 10.1109/tac.2004.838492 |
| Reference:
|
[7] Byrnes, C. I., Priscoli, F. D., Isidori, A.: Output regulation of uncertain nonlinear systems..Springer Science and Business Media, 2012. MR 2742099, 10.1007/978-1-4612-2020-6 |
| Reference:
|
[8] Davison, E.: The robust control of a servomechanism problem for linear time-invariant multivariable systems..IEEE Trans. Automat. Control 21 (1976), 1, 25-34. MR 0406616, 10.1109/tac.1976.1101137 |
| Reference:
|
[9] Duan, G. R., Yu, H. H.: LMIs in Control Systems: Analysis, Design and Applications..CRC Press, 2013. MR 3328859 |
| Reference:
|
[10] Ltd, Feedback instruments, Manual, East Sussex. TRMS 33-949S User: Twin Rotor MIMO System Control Experiments, 1998.. |
| Reference:
|
[11] Francis, B. A.: The linear multivariable regulator problem..SIAM J. Control Optim. 15 (1077), 486-505. MR 0446631, 10.1137/0315033 |
| Reference:
|
[12] Francis, B. A., Wonham, W. M.: The internal model principle for linear multivariable regulators..J. Appl. Math. Optim. 2 (1975), 170-194. MR 0389331, 10.1007/bf01447855 |
| Reference:
|
[13] Glauser, M., Lin, Z., Allaire, P. E.: Modeling and control of a partial body weight support system: an output regulation approach..IEEE Trans. Control Systems Technol. 18 (2010), 2, 480-490. 10.1109/tcst.2009.2016953 |
| Reference:
|
[14] Henriques, J., Gil, P., Cardoso, A., Carvalho, P., Dourado, A.: Adaptive neural output regulation control of a solar power plant..Control Engrg. Practice 18 (2010), 10, 1183-1196. 10.1016/j.conengprac.2010.06.001 |
| Reference:
|
[15] Isidori, A.: Nonlinear Control Systems. Third edition..Springer, London 1995. MR 1410988, 10.1007/978-1-84628-615-5 |
| Reference:
|
[16] Isidori, A., Byrnes, C. I.: Output regulation of nonlinear systems..{IEEE} Trans. Automat. Control 35 (1990) 2, 131-140. Zbl 0989.93041, MR 1038409, 10.1109/9.45168 |
| Reference:
|
[17] Jensen, T. N., Wisniewski, R., DePersis, C., Kallesøe, C. S.: Output regulation of large-scale hydraulic networks with minimal steady state power consumption..Control Engrg. Practice 22 (2014), 103-113. 10.1016/j.conengprac.2013.10.004 |
| Reference:
|
[18] Khalil, H.: Nonlinear Systems. Third edition..Prentice Hall, New Jersey 2002. |
| Reference:
|
[19] Kim, W., Kim, H., Chung, C. C., Tomizuka, M.: Adaptive output regulation for the rejection of a periodic disturbance with an unknown frequency..IEEE Trans. Control Systems Technol. 19 (2011), 5, 1296-1304. 10.1109/tcst.2010.2066276 |
| Reference:
|
[20] Lewis, F. L., Dawson, D. M., Abdallah, C. T.: Robot Manipulator Control: Theory and Practice..CRC Press, 2003. 10.1201/9780203026953 |
| Reference:
|
[21] Mahony, R., Mareels, I., Bastin, G., Campion, G.: Static-state feedback laws for output regulation of non-linear systems..Control Engingrg. Practice 4 (1966), 7, 1009-1014. 10.1016/0967-0661(96)00100-1 |
| Reference:
|
[22] Marconi, L., Praly, L.: Uniform practical nonlinear output regulation..IEEE Trans. Automat. Control 53 (2008), 5, 1184-1202. MR 2445674, 10.1109/tac.2008.923674 |
| Reference:
|
[23] Meda, J. A., Castillo, B.: Synchronization of chaotic systems from a fuzzy regulation approach..Fuzzy Sets Systems 160 (2009), 19, 2860-2875. MR 2573363, 10.1016/j.fss.2008.12.006 |
| Reference:
|
[24] Meda, J. A., Gomez, J. C., Castillo, B.: Exact output regulation for nonlinear systems described by {Takagi}-{Sugeno} fuzzy models..{IEEE} Trans. Fuzzy Systems 20 (2012), 2, 235-247. 10.1109/TFUZZ.2011.2172689 |
| Reference:
|
[25] Nejjari, F., Rotondo, D., Puig, V., Innocenti, M.: LPV modelling and control of a Twin Rotor MIMO system..In: 19th Mediterranean Conference on Control and Automation (MED), IEEE 2011, pp. 1082-1087. 10.1109/med.2011.5983178 |
| Reference:
|
[26] Pandey, S. K., Laxmi, V.: Optimal control of twin rotor MIMO system using LQR technique..Comput. Intell. Data Mining 31 (2015), 11-21. 10.1007/978-81-322-2205-7_2 |
| Reference:
|
[27] Pavlov, A., Janssen, B., Wouw, N. Van de, Nijmeijer, H.: Experimental Output Regulation for a Nonlinear Benchmark System..IEEE Trans. Control Systems Technol. 15 (2007), 4, 786-793. MR 2190284, 10.1109/tcst.2006.890294 |
| Reference:
|
[28] Pratap, B., Purwar, S.: Neural network observer for twin rotor mimo system: an lmi based approach..In: The 2010 International Conference on Modelling, Identification and Control (ICMIC), IEEE 2010, pp. 539-544. |
| Reference:
|
[29] Robles, R., Bernal, M.: Comments on Exact output regulation for nonlinear systems described by Takagi-Sugeno fuzzy models..IEEE Trans. Fuzzy Systems 23 (2015), 1, 230-233. 10.1109/tfuzz.2014.2321773 |
| Reference:
|
[30] Tanaka, K., Wang, H. O.: Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach..John Wiley and Sons, New York 2001. 10.1002/0471224596 |
| Reference:
|
[31] Tao, C.-W., Taur, J.-S., Chang, Y.-H., Chang, C.-W.: A novel fuzzy-sliding and fuzzy-integral-sliding controller for the twin-rotor multi-input-multi-output system..IEEE Trans. Fuzzy Systems 18 (2010), 5, 893-905. 10.1109/tfuzz.2010.2051447 |
| Reference:
|
[32] Tapia, A., Márquez, R., Bernal, M., Cortez, J.: Sliding subspace design based on linear matrix inequalities..Kybernetika 50 (2014), 3, 633-641. MR 3245539 |
| Reference:
|
[33] Tarn, T. J., Sanposh, P., Cheng, D., Zhang, M.: Output Regulation for Nonlinear Systems: Some Recent Theoretical and Experimental Results..IEEE Trans. Control Systems Technol. 13 (2005), 605-610. 10.1109/tcst.2004.841674 |
| Reference:
|
[34] Umemura, Y., Sakamoto, N.: Optimal servo design for lock-up slip control for torque converter nonlinear output regulation approach..IEEE Trans. Control Systems Technol. 23 (2015), 4, 1587-1593. 10.1109/tcst.2014.2366077 |
| Reference:
|
[35] Yoon, S. Y., Di, L., Lin, Z.: Unbalance compensation for AMB systems with input delay: An output regulation approach..Control Engrg. Practice 46 (2016), 166-175. MR 3318613, 10.1016/j.conengprac.2015.11.002 |
| . |
